Reissner厚板弹性弯曲的一般解析解

针对大型工程建设中的Reisner厚板弹性弯曲问题,本文采用复级数方法求解相应的常系数偏微分方程组的边值问题,并首次得到了任意边界条件下的一般解析解.该解形式简单,计算方便、可靠.以四边简支和三边固支一边自由两种支撑条件下厚板承受均布载荷为例进行了分析验算,与已有的计算结果相比,计算结果相当满意.同时本文还着重对解的收敛速度、正确性(合理性)及边界满足情况进行了考察.

General Analytic Solution for Elastic Bending of Reissner Plates

In this paper, by developing the complex Fourier series method to solve the boundary value problem of a system of partial differential equations with constant coefficients, for the first time a general analytic solution satisfying an arbitrary boundary condition is presented for the elastic bending of thick Reissner plates in engineering. The solution is simple and convenient to programming. Analysis and computation are performed for the uniformly loaded plates under two different supporting conditions(four simply supported edges or three clamped and one free edges), the results of which are fairly satisfactory in comparison wit h those available for reference. And at the same time the analytic solution has been investigated mainly in three aspects:a) speed of convergence; b) reliability(rationality); c)fitting of boundary conditions.